Path Integral Calculation of Quantum Nonadiabatic Rates in Model Condensed Phase Reactions

We present accurate path integral calculations of quantum rate constants for model nonadiabatic reactions in condensed matter. The model is described by two coupled diabatic potential surfaces interacting linearly with a bath of harmonic oscillators. The rate constant is obtained from the time integral of the flux−flux correlation function which is evaluated by the quasi-adiabatic propagator path integral method. We study the dependence of the reaction rate on friction, temperature, and exothermicity and compare with predictions of analytical theories. In particular, we observe a broad golden rule plateau as well as rate enhancement due to quantum resonances for low friction in agreement with the semiclassical analysis of Onuchic and Wolynes.